Yes, they do exist. There's a large number of existing instances, some better than others (and suited to different people and their needs)
There's no need to stay put in a place you are not happy or comfortable with.
Basic options are :
This is the easiest option. Many possibilities, and you don't need to get into the nitty gritty of setting up a full instance, maintaining it.
Have taken this route myself, dissatisfied with things at a place I previously called home. Now, I have found a small instance which I am pleased with, and written about it on my blog.
or, the next step up...
My friend @realcaseyrollins took this route, and looking at his instance's front page, it looks nice.
He used the CofeSpace service, which highly simplifies the instance creation - automating most of it, and hosting it for you as well. I believe this was created and is run by P, the admin of the well known FreeSpeechExtremists instance. CofeSpace's Terms of Service are here
The setup is done via the main page -- fill in a few requested items, and it could soon be up and running. These instances are driven by Pleroma, and benefit from it's light and agile performance, plus the many features like Rich Text support (Markdown, HTML and BBcode are supported) that it has.
or, if you are brave and want full independance,
Google cloud or others offer up to one year of free service. You can install Pleroma, configure it from scratch.
Her personal instance is set up and running as described - and is located here.
I wanted to mention this and thank those fedi friends for sharing their experiences.
#FediReporter on alternatives to staying put. Don't. Follow your heart.
See also : Discover Pleroma, an Alternative to Mastodon
Ein kostenloses und werbefreies soziales Netzwerk für Personen aus Münster und Umgebung - und auch alle anderen!